Final answer:
To change the order of integration in a calculator, identify the current limits, sketch the region of integration, re-establish new limits for the reverse order, and then enter the new integral into the calculator, using functions like those on the TI series for computation.
Step-by-step explanation:
To use a calculator to change the order of integration in a double or triple integral, you need to understand the region of integration and the functions that bound this region. When changing the order of integration, you effectively alter how you view the region by flipping the order in which you integrate with respect to the variables. Let's go through a step-by-step process for changing the order of a double integral as an example:
- Identify the limits of integration for the original order.
- Determine the geometry of the region of integration, which could be achieved by sketching it.
- Based on the sketch, re-establish the limits of integration for the new order by finding the bounding functions relevant to the new order of variables.
- Enter the new integral into the calculator with the updated limits of integration. Depending on the calculator model, you may use a function like the TI-83, 83+, or 84's integral function to input the new bounds and integrand.
In many calculators, changing the order of integration is not automated and requires your understanding of the integral's geometry. However, once the new limits are determined, entering them into the calculator following the respective syntax will allow for computation.
Significance: Understanding how to change the order of integration is crucial for evaluating complex integrals that might be simpler in a different order, or when the integrand is more easily integrated with respect to one variable before another.